System and method for determining whether there is an anomaly in data

ABSTRACT

A system and method for identifying objects of interest in image data is provided. The present invention utilizes principles of Iterative Transformational Divergence in which objects in images, when subjected to special transformations, will exhibit radically different responses based on the physical, chemical, or numerical properties of the object or its representation (such as images), combined with machine learning capabilities. Using the system and methods of the present invention, certain objects that appear indistinguishable from other objects to the eye or computer recognition systems, or are otherwise almost identical, generate radically different and statistically significant differences in the image describers (metrics) that can be easily measured.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/374,611 filed on Mar. 14, 2006, now abandoned, which is acontinuation-in-part of U.S. patent application Ser. No. 11/136,406filed on May 25, 2005, now U.S. Pat. No. 7,496,218, and acontinuation-in-part of U.S. patent application Ser. No. 11/136,526filed on May 25, 2005, now U.S. Pat. No. 7,492,937. U.S. patentapplication Ser. Nos. 11/136,406 and 11/136,526 each claim priority toProvisional Application No. 60/574,220, filed on May 26, 2004,Provisional Application No. 60/574,221, filed on May 26, 2004,Provisional Application No. 60/578,872, filed on Jun. 14, 2004 andProvisional Application No. 60/661,477, filed on Mar. 15, 2005.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to image analysis and, more specifically, to asystem and method for identifying objects of interest in image data.This includes, but is not limited to a methodology for accomplishingimage segmentation, clarification, visualization, feature extraction,classification, and identification.

2. Background of the Related Art

Computer-aided image recognition systems rely solely on the pixelcontent contained in a two-dimensional image. The image analysis reliesentirely on pixel luminance or color, and/or spatial relationship ofpixels to one another. In addition, image recognition systems utilizeanalysis methodologies that often assume that distinctivecharacteristics of objects exist and can be differentiated.

However, most real-world image analysis problems involve limitations inaccurately segmenting/classifying the objects. The following are some ofthe specific issues limiting existing image analysis methodologies:

(1) input data (image objects) need to be transformed into structureddata type;

(2) did not adjust for proper combination of scale, rotation,perspective, size, etc.;

(3) classes of objects need to be distinguishable using the image or itsrepresentation;

(4) Grayscale image analysis still represents a serious problem in someapplications.

(5) Color processing can be very computationally intensive.

SUMMARY OF THE INVENTION

An object of the invention is to solve at least the above problemsand/or disadvantages and to provide at least the advantages describedhereinafter.

Therefore, an object of the present invention is to provide a systemcapable of detecting objects of interest in image data with a highdegree of confidence and accuracy.

Another object of the present invention is to provide a system andmethod that does not directly rely on predetermined knowledge of anobjects shape, volume, texture or density to be able to locate andidentify a specific object or object type in an image.

Another object of the present invention is to provide a system andmethod of identifying objects of interest in image data that iseffective at analyzing images in both two- and three-dimensionalrepresentational space using either pixels or voxels.

Another object of the present invention is to provide a system andmethod of distinguishing a class of known objects from objects ofsimilar color and texture whether or not they have been previouslyexplicitly observed by the system.

Another object of the present invention is to provide a system andmethod of identifying objects of interest in image data that works withvery difficult to distinguish/classify image object types, such as: (i)apparent random data; (ii) unstructured data; and (iii) different objecttypes in original images.

Another object of the present invention is to provide a system andmethod of identifying objects of interest in image data that can causeeither convergence or divergence (clusterization) of explicit orimplicit image object characteristics that can be useful in creatingdiscriminating features/characteristics.

Another object of the present invention is to provide a system andmethod of identifying objects of interest in image data that canpreserve object self-similarity during transformations.

Another object of the present invention is to provide a system andmethod of identifying objects of interest in image data that is stableand repeatable in its behavior.

To achieve the at least above the objects, in whole or in part, there isprovided a method for determining whether there is an anomaly in data,comprising performing one of applying a bifurcation transform to thedata, mapping the data to a predetermined color space and mapping thedata to a feature space to yield altered data, and comparing the altereddata with a template of altered data created from a set of data notcontaining the anomaly to determine whether there is a differencebetween the altered data and the template, said difference correspondingto said anomaly.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objects and advantages of the invention may be realizedand attained as particularly pointed out in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Patent Office upon request andpayment of the necessary fee.

The invention will be described in detail with reference to thefollowing drawings, in which like reference numerals refer to likeelements, wherein:

FIG. 1 is a bifurcation diagram;

FIG. 2 is a diagram illustrating how three complementary paradigms areused to obtain intelligent image informatics, in accordance with oneembodiment of the present invention;

FIG. 3 is a block diagram of a system for identifying an object ofinterest in image data, in accordance with one embodiment of the presentinvention;

FIGS. 4A-5C are transfer functions applied to the pixel color of theimage, in accordance with the present invention;

FIG. 6A is an input x-ray image of a suitcase, in accordance with thepresent invention;

FIG. 6B is the x-ray image of FIG. 6 a after application of the imagetransformation divergence process of the present invention;

FIG. 7 is a block diagram of an image transformation divergence systemand method, in accordance with one embodiment of the present invention;

FIGS. 8A-8M are x-ray images of a suitcase at different stages in theimage transformation recognition process of the present invention;

FIG. 8N is an example of a divergence transformation applied to an x-rayimage during the image transformation divergence process of the presentinvention;

FIG. 9 is an original input medical image of normal and cancerous cells;

FIG. 10 is the image of FIG. 9 after application of the imagetransformation recognition process of the present invention;

FIG. 11 is an original input ophthalmology image of a retina;

FIG. 12 is the image of FIG. 11 after application of the imagetransformation recognition process of the present invention;

FIG. 13 is a flowchart of a method of creating a Support Vector Machinemodel, in accordance with one embodiment of the present invention;

FIG. 14 is a flowchart of a method of performing a Support VectorMachine operation, in accordance with one embodiment of the presentinvention;

FIGS. 15A-15C are medical x-ray images;

FIGS. 16A and 16B are x-ray images from a Smith Detection (Smith) x-rayscanner and a Rapiscan x-ray scanner, respectively;

FIG. 17 is a schematic diagram of an x-ray scanner;

FIG. 18 is a schematic diagram of an x-ray source used in the x-rayscanner of FIG. 17;

FIGS. 19A and 19B are X-ray images from a Smith scanner and a Rapiscanscanner, respectively, which illustrate geometric distortions withcolors;

FIG. 20 is a schematic diagram of an x-ray scanner;

FIG. 21 is a plot of (P,C) space with Zeff ((P,C)=const.;

FIG. 22 is a plot showing a 3D view of (P,C) space with Zeff(P,C)=const,

FIGS. 23A and 23B are plots showing 2D and 3D view of (P,C) space withd(P,C)=const,

FIG. 24A is a plot showing an RGB_DNA 3×2D view for a Smith HiScan 6040iscanner;

FIG. 24B is a plot showing an RGB_DNA 3×2D view for a Rapiscan 515scanner;

FIG. 25A is a plot showing an RGB_DNA 3D view for a Smith HiScan 6040iscanner;

FIG. 25B is a plot showing an RGB_DNA 3D view for a Rapiscan 515scanner;

FIG. 26 are plots showing the modeling of 2D (P,C) space on the left and3D RGB_DNA on the right for a Smith scanner;

FIG. 27 are plots showing the sequence of (P,C) 2D elastictransformation to RGB_DNA (and back);

FIG. 28 is a plot of a 2D (P,C) representation of a Smith RGB_DNA set ofunique colors;

FIG. 29 is a plot showing the color curve(s) of Zeff=const on the SmithRGB_DNA;

FIG. 30 is a schematic diagram of an x-ray scanner with an object to bescanned that consists of multiple layers of materials;

FIG. 31 is a plot showing 2D (P,C) space with vector addition;

FIG. 32 is a plot showing a color algebra example for a Smithcalibration bag consisting of overlapped materials;

FIG. 33 are examples of images with their 3D RGB_DNA views;

FIG. 34 are plots showing incorrect RGB_DNA as a result of accidentalconversion from 24-bit bmp to 16-bit bmp and back to 24 bit bmp;

FIG. 35 are plots showing the fine structure of z-lines on their wayfrom the central region of the 3D RGB cube towards the black pole withRGB=(0,0,0);

FIG. 36 is a plot showing the z-lines shown in FIG. 35 from the point inRGB space lying on the prolongation of the major diagonal of RGB cube

FIG. 37 are plots showing examples of extracted z-lines and theirscolors in 3×2D RGB_DNA view;

FIG. 38 are plots showing extracted z-lines number 1, 7 and 25 andtheirs colors in 3D RGB_DNA view;

FIG. 39 is a plot showing the fragment of typical 25 bin's z-metrics for1^(st) nine z-lines;

FIG. 40 are organic only, normal and metal only images and theirrespective 3D RGB_DNA;

FIG. 41 shows an original image and its RGB_DNA with no filters applied;

FIG. 42 shows the image of FIG. 41 with a z-filter applied to keep lightorganics;

FIG. 43 shows the image of FIG. 41 with a z-filter applied to keep heavyorganics;

FIG. 44 shows the image of FIG. 41 with a z-filter applied to keep heavyorganics and metal; and

FIG. 45 shows the image of FIG. 41 with a z-filter applied to keep lightorganics and metal.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Definition of Terms

The following definitions hold throughout the contents of thisapplication. If additional or alternative definitions of the same orsimilar words are provided herein, those definitions should be includedherein as well.

“Statistically identical” or “statistically indistinguishable”: Two setsof data are referred to as “statistically identical” or “statisticallyindistinguishable” if under one or more types of statistics orobservation there is almost no discernable difference between them.

Point operation: Point operation is a mapping of a plurality of datafrom one space to another space which, for example, can be apoint-to-point mapping from one coordinate system to a differentcoordinate system. Such data can be represented, for example, bycoordinates such as (x, y) and mapped to different coordinates (α, β)values of pixels in an image.

Z effective (Z_(eff)): Is the effective atomic number for amixture/compound of elements. It is an atomic number of a hypotheticaluniform material of a single element with an attenuation coefficientequal to the coefficient of the mixture/compound. Z effective can be afractional number and depends not only on the content of themixture/compound, but also on the energy spectrum of the x-rays.

Divergence: The movement or spreading of points in vector space fromwithin a local neighborhood (vicinity) to radically different values orlocations.

“Divergence transform” or “bifurcation transform”: The phrases“divergence transform” and “bifurcation transform” are usedinterchangeably and each results from a nonlinear or discontinuousremapping of points in vector space which when operating on data such asan entire image, image segment, or subset of an image, causesinformation relating to the content of the data that otherwise would nothave been readily or easily apparent to become available or more easilyapparent or accessible.

“Divergence transformation” or “bifurcation transformation”: The phrases“divergence transformation” and “bifurcation transformation” are usedinterchangeably and refer to a transform which, when operating on datasuch as a segment or subset of an image, causes information relating tothe content of the data that otherwise would not have been readily oreasily apparent to become available or more easily apparent oraccessible. The intent of the transform is to cause a bifurcation of theimage data.

For example, when applying a divergence transformation to an image or asegment of the image, information regarding the contents of the imagewhich would not have been easily recognized prior to application of thedivergence transformation becomes more apparent or known. For example,two objects in the same image that are almost indistinguishable becomedistinguishable after the divergence transformation is applied.

Hyperspectral data: Hyperspectral data is data that is obtained from aplurality of sensors at a plurality of wavelengths or energies. A singlepixel or hyperspectral datum can have hundreds or more values, one foreach energy or wavelength. Hyperspectral data can include one pixel, aplurality of pixels, or a segment of an image of pixels, etc., with saidcontent. As contained herein, it should be noted that hyperspectral datacan be treated in a manner analogous to the manner in which dataresulting from a divergence transformation is treated throughout thisapplication for systems and methods for threat or object recognition,identification, image normalization and all other processes and systemsdiscussed herein.

For example, a divergence transformation can be applied to hyperspectraldata in order to extract information from the hyperspectral data thatwould not otherwise have been apparent. Divergence transformations canbe applied to a plurality of pixels at a single wavelength ofhyperspectral data or multiple wavelengths of one or more pixels ofhyperspectral data in order to observe information that would otherwisenot have been apparent.

Nodal point: A nodal point is a point in an image transformation orseries of image transformations where similar pixel values exhibit asignificantly distinguishable change in value. Pixels are a unitaryvalue within a 2D or multi-dimensional space (such as a voxel).

Object: An object can be a person, place or thing.

Object of interest: An object of interest is a class or type of objectsuch as explosives, guns, tumors, metals, knives, camouflage, etc. Anobject of interest can also be a region with a particular type of rocks,vegetation, etc.

Threat: A threat is a type of object of interest which typically but notnecessarily could be dangerous.

Image receiver: An image receiver can include a process, a processor,software, firmware and/or hardware that receives image data.

Image mapping unit: An image mapping unit can be a processor, a process,software, firmware and/or hardware that maps image data to predeterminedcoordinate systems or spaces.

Comparing unit: A comparing unit can be hardware, firmware, software, aprocess and/or processor that can compare data to determine whetherthere is a difference in the data.

Color space: A color space is a space in which data can be arranged ormapped. One example is a space associated with red, green and blue(RGB). However, it can be associated with any number and types of colorsor color representations in any number of dimensions.

HSI color space: A color space where data is arranged or mapped by Hue,Saturation and Intensity.

Predetermined color space: A predetermined color space is a space thatis designed to represent data in a manner that is useful and that could,for example, cause information that may not have otherwise been apparentto present itself or become obtainable or more apparent.

RGB DNA: RGB DNA refers to a representation in a predetermined colorspace of most or all possible values of colors which can be producedfrom a given image source. Here, the values of colors again are notlimited to visual colors but are representations of values, energies,etc., that can be produced by the image system.

Signature: A signature is a representation of an object of interest or afeature of interest in a predetermined space and a predetermined colorspace. This applies to both hyperspectral data and/or image data.

Template: A template is part or all of an RGB DNA and corresponds to animage source or that corresponds to a feature or object of interest forpart or all of a mapping to a predetermined color space.

Algorithms: From time to time, transforms and/or divergencetransformations are referred to herein as algorithms.

Algorithms and systems discussed throughout this application can beimplemented using software, hardware, and firmware.

Modality: any of the various types of equipment or probes used toacquire images. Radiography, CT, ultrasound and magnetic resonanceimaging are examples for modalities in this context.

The analysis capabilities of the present invention can apply to amultiplicity of input devices created from different electromagnetic andsound emanating sources such as ultraviolet, visual light, infra-red,gamma particles, alpha particles, etc.

Image Transformation Divergence System and Method General Overview

The present invention identifies objects of interest in image datautilizing image conditioning and data analysis in a process hereintermed “Image Transformation” (ITR) or, equivalently, “ImageTransformation Divergence” (ITD). The terms ITR and ITD refer to thesame process, and may be used interchangeably herein.

The ITD process can cause different yet almost identical objects in asingle image to diverge in their measurable properties. An aspect of thepresent invention is the discovery that objects in images, whensubjected to special transformations, will exhibit radically differentresponses based on the pixel values of the imaged objects. Using thesystem and methods of the present invention, certain objects that appearalmost indistinguishable from other objects to the eye or computerrecognition systems, or are otherwise identical, generate radicallydifferent and significant differences that can be measured.

Another aspect of the present invention is the discovery that objects inimages can be driven to a point of non-linearity by certaintransformation functions. The transformation functions can be appliedsingly or in a sequence, so that the behavior of the system progressesfrom one state through a series of changes to a point of rapid departurefrom stability called the “point of divergence.”

FIG. 1 is an example of a bifurcation diagram illustrating iterativeuses of divergence transforms, where each node represents an iterationor application of another divergence transform. A single image isrepresented as a simple point on the left of the diagram. There areseveral branches in the diagram (at lines A, B and C) as the lineprogresses from the original image representation on the left,indicating node points where bifurcation occurs (“points ofbifurcation”). In this example, three divergence transforms were used inseries at points A, B and C. In this example, each divergence transformresults in a bifurcation of the image objects or data. At point A, someobjects that are very dissimilar from the objects of interest divergeaway from the most likely object of interest candidates (e.g., threatvs. non-threat, malignant vs. benign tumor, vegetation vs. camouflage,etc.). This is defined mathematically as reaching a “Repellor Point.”

At point B, additional objects are rejected and diverge away from theremaining object of interest candidates. At point C, the search isfurther refined and additional objects are rejected and diverge awayfrom the remaining object of interest candidates. This spatial filteringprocess is analogous to applying narrower and narrower band pass filtersin the frequency domain.

At a certain number of iterations (beyond point C in this example), theobject integrity may deteriorate or no further improvement in thedetection process is realized. At this point, other methodologies, e.g.,Machine Learning Algorithms (MLAs) may be applied to further distinguishthe objects of interest from other object of interest candidates.

Another aspect of the present invention is that one can apply the“principle of divergence” to the apparent stability of fixed points orpixels in an image and, by altering one or more parameter values, giverise to a set of new, distinct and clearly divergent image objects.Because each original object captured in an image responds uniquely atits point of divergence, the methods of the present invention can beused in an image recognition system to distinguish and measure objects.It is particularly useful in separating and identifying objects thathave almost identical color, density and volume.

The system and methods of the present invention provides at least thefollowing advantages over prior image extraction methodologies:

(1) It is a system capable of detecting objects with a high degree ofconfidence;

(2) It does not rely only on a prior knowledge of an objects shape,volume, texture or density to be able to locate and identify a specificobject or object type in the image;

(3) It is effective at analyzing images in multi-dimensionalrepresentational space using either pixels or voxels;

(4) It is most powerful where a class of known objects is to bedistinguished from objects of similar color and texture, whether or notthey have not been previously observed or trained by the ITD system;

(5) It works with very difficult to distinguish/classify image objecttypes, such as different object types in original images (threats andnon-threats for example or different types of threats) have almostindistinguishable differences between their features when analyzed;

(6) It can more effectively apply statistical analysis tools todistinguish data;

(7) It can cause either convergence or divergence of image objectfeatures;

(8) It can preserve object geometrical integrity during transformations;and

(9) It is stable and repeatable in its behavior.

In one exemplary embodiment of the present invention, specialtransformations are applied to images in an iterative “filter chain”sequence. The nature of the sequence of transforms causes objects in theimage to exhibit radically different responses based on their pixelvalue(s) such as color (that are related to the physical propertiesinherent in the original objects in the image). Using the sequencingprocess, certain objects that appear almost indistinguishable to the eyeor computer recognition systems from other objects, generate radicallydifferent and significant differences that can be easily measured.

As transform parameters are increased, the behavior of the objectsprogresses from one of simple stability, through a sequence of changes,to a state of a unique and radical change. The state of unique andradical change comes about due to a characteristic “signature”associated with the object of interest's interaction with the sourceused to create the image. These signatures are exploited by adapting thedivergence transforms of the present invention.

The ITD process works with an apparently stable set of fixed points orpixels in an image and, by altering one or more parameter values, givingrise to a set of new, distinct, and clearly divergent image objects.Commonly used and understood transforms work within the domain whereimages maintain equilibrium.

As will be discussed in more detail below, the ITD method starts byfirst segmenting the image into objects of interest, then applyingdifferent filter sequences to the same original pixels in the identifiedobjects of interest using the process. In this way, the process is notlimited to a linear sequence of filter processing.

Because of the unique nature of the segmentation process using thisiterative approach, objects within objects can be examined. As anexample, an explosive inside of a metal container can be located byfirst locating all containers, remapping the original pixel data withknown coordinates in the image and then examining the remapped originalpixels in the identified object(s) in the image for threats withadditional filter sequences.

With the ITD process, transforms can be tuned to optimize thedistinction of the object of interest of the images. In addition, theprocess works for both image segmentation and feature generation throughan iterative process of applying image transforms. As discussed above,it is defined mathematically as a reaching a Repellor Point.

An aspect of the present invention is the use of three complementaryparadigms to extract information out of images that would otherwise notbe readily available. This process is herein referred to as “IntelligentImage Informatics”. As illustrated in FIG. 2, the three complementaryparadigms include: (1) Image Processing; (2) Pattern Classification(Contextual Imagery with Machine Learning); and (3) ψ—Physics.

Imaging can take place in the spatial domain, spectral domain, RGB_DNAspace and/or feature space. The Feature Extraction Process can use theimage's describers/qualifiers/characteristics from the above mentioneddomains. These feature can be analyzed by many pattern classificationtechniques, also called Machine Learning Algorithms such as SupportVector Machines (SVM), decision trees/graphs. ψ—Physics refers to thephysics that governs the image source, such as dual energy scanningsystems, the z-effective exhibited by different materials and theRGB_DNA that characterizes the image source. All of these methodologiesand concepts will be explained in more detail below.

The ITD methodologies of the present invention reveal signatures inradiographic image objects that have been previously invisible to thehuman eye. The application of specific non-linear functions to agrey-scale or color radiographic images is the basis of ITD. Due to theCompton and photoelectric effects, objects in the image exhibit unique,invariant responses to the ITD algorithms based on their physicalinteractions with the electromagnetic beam. By applying a combination ofcomplementary functions in an iterative fashion, objects of very similargrey-scale or color content in the original image significantly divergeat a point of non-linearity. This divergence causes almost statisticallyequivalent objects in the original image to display significant density,color and pattern differences. Different algorithms are used fordistinguishing objects that exhibit different ranges of effective atomicnumbers (Z_(eff)). The algorithms are tuned to be optimal within certainfractional ranges of resultant electromagnetic Compton/photoelectriccombinations.

Both spatial and spectral analysis is utilized. The probability ofachieving accurate results can be improved by utilizing multiple passes.With each run of the ITD process, a new hyperplane of image pixel datais created for each object. The combination of the original image plusthe newly-created hyperplanes is mapped to form a multi-spectralhypercube. The hypercube has pixel dimensions P_(n) where n is the totalnumber of outputs from all iterations.

The hypercube now contains spectral bands for each object that are theresult of the object's response to each ITD iteration. This is quitesimilar to the creation of hyperspectral data that is collected bysensors from the reflectance of objects. The hypercube data containsboth spatial and spectral components that can be used for effectivepattern classification rule generation.

Empirical testing has shown that objects retain their characteristic“response-based signatures” for a wide range of fractionalCompton/photoelectric results, even when there is significant pixelmixing due to overlapping of other objects. This should not becompletely unexpected since differences in a given object's thicknesscan generate the same Z_(eff) with the variability being expressed as achange in density.

Exemplary Embodiments A. General System and Method for Identifying anObject of Interest

FIG. 3 is a block diagram of a system 100 for identifying an object ofinterest in image data, in accordance with one embodiment of the presentinvention. The system 100 comprises an input channel 110 for inputtingimage data 120 from an image source (not shown) and an image analysissystem 130. In one preferred embodiment of the present invention, theimage analysis system 130 generates transformed image data utilizingITD, in which the object of interest is distinguishable from otherobjects in the image data.

The object of interest can be any type of object. For example, theobject of interest can be a medical object of interest, in which casethe image data can be computer tomography (CT) image data, x-ray imagedata, or any other type of medical image data. As another example, theobject of interest can be a threat object, such as weapons, explosives,biological agents, etc., that may be hidden in luggage. In the case, theimage data is typically x-ray image data from luggage screeningmachines.

At least one divergence transformation, preferably a point operation, ispreferably utilized in the image analysis system 130. A point operationconverts a single input image into a single output image. Each outputpixel's value depends only on the value(s) of its corresponding pixel inthe input image. Input pixel coordinates correlate to output pixelcoordinates such that X_(i), Y_(i)→X_(o), Y_(o). A point operation doesnot change the spatial relationships within an image. This is quitedifferent from local operations where the value of neighboring pixelsdetermines the value of the output pixel.

Point operations can correlate both gray levels and individual colorchannels in images. One example of a point operation is shown in thetransfer function of FIG. 4A. In FIG. 4A, 8 bit (256 shades of gray)input levels are shown on the horizontal axis and output levels areshown on the vertical axis. If one were to apply the point operation ofFIG. 4A to an input image, there would be a 1 to 1 correlation betweenthe input and the output (transformed) image. Thus, input and outputimages would be the same.

Point operations are predictable in how they modify the histogram of animage. Point operations are typically used to optimize images byadjusting the contrast or brightness of an image. This process is knownas contrast enhancing. They are typically used as a copying technique,except that the pixel values are modified according to the specifiedtransfer function. Point operations are also typically used forphotometric calibration, contrast enhancement, monitor displaycalibration, thresholding and clipping to limit the number of levels ofgray in an image. The point operation is specified by the transformationfunction ƒ and can be defined as:B(x,y)=ƒ[A(x,y)],

where A is an input image and B is an output image.

The at least one divergence transformation used in the image analysissystem 130 can be either linear or non-linear point operations, or both.Non-linear point operations are used for changing thebrightness/contrast of a particular part of an image relative to therest of the image. This can allow the midpoints of an image to bebrightened or darkened while maintaining blacks and white in thepicture.

FIG. 4B is a linear transfer function, and FIGS. 4C-4E illustratetransformations of some non-linear point operations. An aspect of thepresent invention is the discovery that the transfer function can beused to bring an images to a point where two initially close colorsbecome radically different after the application of the transferfunction. This typically requires a radical change in the output slopeof the resultant transfer function of FIG. 5A.

The present invention preferably utilizes radical luminance (grayscale),color channel or a combination of luminance and color channel transferfunctions to achieve image object differentiation for purposes of imageanalysis and pattern recognition of objects. The placement of the nodalpoints in the transfer function(s) is one key parameter. An example ofnodal point placements are shown in the transfer function exampleillustrated in the FIG. 5B. The nodal points in the transfer functionused in the present invention are preferably placed so as to frequentlycreate radical differences in color or luminance between image objectsthat otherwise are almost identical.

This is illustrated in the sample transfer function of FIG. 5C. Usingthis transformation, two objects that are very close in color/luminancein an original image would be on opposite sides of a grayscalerepresentation in the output (transformed) image. FIG. 6A shows an inputimage, and FIG. 6B shows the changes made to the input image (thetransformed image obtained) as a result of applying the transferfunction of FIG. 5C. The input image is an x-ray image of a suitcasetaken by a luggage scanner. In this example, the objects of interest areshoes 300 and a bar of explosives 310 on the left side of the suitcase.

Note that the orange background has gone a very different color from theshoes 300 and the bar 310 on the left side of the suitcase. The transferfunction of FIG. 5C uniquely delineates the objects of interest, whileeliminating the background clutter in the image.

As can be seen by the input and transformed images shown in FIGS. 6A and6B, respectively, the orange background in the image makes a radicaldeparture from the orange objects of interest (300 and 310) and otherobjects that are almost identical to the objects of interest. The use ofdifferent nodal points in the transfer function will cause the objectsof interest to exhibit a different color from other objects.

Data points connecting the nodes can be calculated using severalestablished methods. A common method of mathematically calculating thedata points between nodes is through the use of cubic splines.

Additional imaging processes are preferably applied in the process ofobject recognition to accomplish specific tasks. Convolutions such asmedian and dilate algorithms cause neighboring pixels to behave insimilar ways under the transfer function, and may be applied to assurethe objects' integrity during the transformation process.

FIG. 7 is a block diagram of one preferred embodiment of the imageanalysis system 130 of FIG. 3, along with a flowchart of a method foridentifying an object of interest in image data using the image analysissystem 130. The image analysis system 130 includes an image conditioner2000 and a data analyzer 3000.

Some of the method steps will be explained with reference to the imagesshown in FIGS. 8A-8M, which are x-ray images of a suitcase at differentstages in the image analysis process. These images are just one exampleof the types of images that can be analyzed with the present invention.Other types of images, e.g., medical images from X-ray machines or CTscanners, or quantized photographic images can also be analyzed with thesystem and methods of the present invention.

The method starts at step 400, where image may optionally be normalized.The normalization process preferably comprises the following processes:(1) referencing; (2) benchmarking; (3) conformity process; and (4)correction process.

The referencing process is used to get a reference image containing anobject of interest for a given type of X-ray machine. This processconsists of passing a container containing one or more objects ofinterest into a reference X-ray machine to get a reference image. Thereferencing process is preferably performed once for each X-ray machinemodel/type/manufacturer.

The benchmarking process is used to get a transfer function used toadjust the colors of the reference image taken by a given X-ray machinethat is not the reference X-ray machine. This process consists ofpassing a reference container into any given X-ray machine to get theimage of this reference container, which is herein referred to as the“current image.” Then, the current image obtained for this X-ray machineis compared with the reference image. The difference between the currentimage and the reference container is made to create a transfer function.

As a transformation of the image's colors of a container, thebenchmarking process determines the transfer function that maps all thecolors of the current image color scheme (“current color scheme”) to thecorresponding colors that are present in the reference color scheme ofthe reference image. The transfer function applied to the current imagetransforms it into the reference image.

The adjustment of the colors of X-ray machines of a differenttype/model/manufacturer requires a distinct and specific calibrationprocess. All X-ray machines are preferably also put through anormalization process. X-ray machines of a same type/model/manufacturerare preferably normalized using the same calibration process. All X-raymachines of different types are preferably calibrated and all themachines, no matter their type, are preferably normalized.

The conformity process is preferably used to correct the image colorrepresentation of any objects that pass through a given X-ray machine.For a given X-ray machine, the conformity process corrects the machine'simage color representation (color scheme) in such a way that the colorscheme of a reference image will fit the reference color scheme of thereference container.

The conformity process preferably consists of applying the transferfunction to each bag that passes into an X-ray machine to “normalize”the color output of the machine. This process is specific to every X-raymachine because of the machine's specific transfer function. Each time acontainer passes through the X-ray machine, the conformity process ispreferably applied.

The correction process is preferably used to correct the images from theX-ray machine. It preferably minimizes image distortions and artifacts.X-ray machine manufacturers use detector topologies and algorithms thatcould have negative effects on the image geometry and colors. Geometricdistortions, artifacts and color changes made by the manufacturer havenegative impacts on images that are supposed to rigorously represent thephysical aspects and nature of the objects that are passed through themachine.

Unlike the conformity process that preferably compensates in a specificway the randomness of the X-ray detector sensitivities of every X-raymachine, the correction process is preferably the same for all X-raymachines of a given model/type/manufacturer.

Next, at step 410, image processing is performed on the image. Manydifferent types of image processing techniques can be used including,but not limited to, ITD, spatial and spectral transformations,convolutions, histogram equalization and gamma adjustments, colorreplacement, band-pass filtering, image sharpening and blurring, regiongrowing, hyperspectral image processing, color space conversion, etc.

In one preferred embodiment, ITD is used for the image processing step410, and as such the image is segmented by applying a color determiningtransform that effect specifically those objects that match a certaincolor/density/effective atomic number characteristics. Objects ofinterest are isolated and identified by their responses to the sequenceof filters. Image segmentation is preferably performed using a series ofsub-steps.

FIGS. 8B-8H show the image after each segmentation sub-step. Theresulting areas of green in FIG. 8G are analyzed to see if they meet aminimum size requirement. This removes the small green pixels. Theremaining objects of interest are then re-mapped to a new whitebackground, resulting in the image of FIG. 8H. Most of the background,organic substances, and metal objects are eliminated in this step,leaving the water bottle 500, fruit 510, peanut butter 520 and object ofinterest 530.

At step 420, features are extracted by the data analyzer 3000 subjectingthe original pixels of the areas of interest identified in step 410 toat least one feature extraction process. It is at this step that atleast one divergence transformation is applied to the original pixels ofthe areas of interest identified in step 410.

In the image examples shown in FIGS. 8I-8M, two feature extractionprocesses are applied. The first process in this example uses thefollowing formulation (in the order listed):

(1) Replace colors

(2) Maximum filter 3×3

(3) Median filter 3×3

(4) Levels and Gamma Luminance=66 black level and 255 white level andGreen levels=189 black, 255 white and gamma=9.9

(5) Apply divergence transformation

(6) Maximum filter 3×3

(7) Replace black with white

(8) Median filter 3×3

The image shown in FIG. 8I results after process step (4) above, theimage shown in FIG. 8J results after process step (5) above, and theimage shown in FIG. 8K results after process step (7) above. Note thatmost of the fruit 510 and the water bottle 500 pixels on the lowerleft-hand side of the image in FIG. 8K have either disappeared or goneto a white color. This is in contrast to the preservation of largeportions of the peanut butter jar 520 pixels and object of interest 530pixels, which are now remapped to a new image in preparation for thesecond feature extraction process (FEP).

At step 430, data conditioning is performed by the data analyzer 3000,in which the data is mathematically transformed to enhance itsefficiency for the MLA to be applied at step 440. In addition, meta datais created (new metrics from the metrics created in the featureextraction step 420 such as the generation of hypercubes. This metadatacan consist of any feature that is derived from the initial featuresgenerated from the spatial domain. Meta data are frequently features ofthe spectral domain, Fourier space, RGB_DNA, and z-effective amongothers.

Machine Learning Algorithms (MLAs) are capable of automatic patternclassification. Pattern classification techniques automaticallydetermine extremely complex and reliable relationships between the imagecharacteristics also called features. These characteristics are use bythe Rules-base that exploits the relationships to automatically detectobject into the images.

At step 440, machine learning algorithms (MLAs) are applied by the dataanalyzer 3000. The feature extraction process of step 420 is applied inorder to represent the images with numbers. The MLAs applied at step 440are responsible for generating the detection system that determines ifan object of interest is present. In order to work properly, MLAs needstructured data types, such as numbers and qualitative/categorical dataas inputs. Since images are unstructured data types, the FeatureExtraction Process is applied to transform the image or segments of animage into numbers. Each number is a metric that represents acharacteristic of the image. Each image is associated with a collectionof the metrics that represents it. The collection of the metrics relatedto an image is herein referred to as a vector. MLAs analyze the vectorof the metrics for all the images and find the metrics' relationshipsthat make up a “rules-base.”

The metrics created by the feature extraction process 420 are used toreflect the image content are, but not limited to, mean, median,standard deviation, rotation cosine measures, kurtosis, Skewness ofcolors and, spectral histogram, co-occurance measures, gabor waveletmeasures, unique color histograms, percent response, and arithmeticentropy measures.

At step 450, the objects are classified by the data analyzer 3000 basedupon the rules-base that classify images into objects of interest andobjects not of interest according to the values of their metrics, whichwere extracted at step 420. As shown in FIG. 8M, the object of interest530 is measured in this process for its orange content. The peanutbutter jar 520 shows green as its primary value, and is thereforerejected.

The detected objects of interest 530 are thus distinguished from allother objects (non-detected objects 470). Steps 410-450 may be repeatedas many times as desired on the non-detected objects 470 in an iterativefashion in order to improve the detection performance.

Determination of distinguishing features between objects of interest andother possible objects is done by the rule-base as a result of theanalysis of the vectors of the metrics by the MLAs applied at step 440.There are hundreds of different MLAs that can be used including, but notlimited to, decision trees, neural networks, support vector machines(SVMs) and Regression.

The rules-base is therefore preferably entered into code and preferablyaccessed from an object oriented scripting language, such as ThreatAssessment Language (TAL). A sample of TAL is shown below.

call show_msg(“C4 Process 3a“) call set_gray_threshold(255) callset_area_threshold(400) callcolor_replace_and(image_wrk,dont_care,dont_care,greater_than,0,0,45,255,255,255)callcolor_replace_and(image_wrk,less_than,dont_care,less_than,128,0,15,255,255,255)call apply_curve(image_wrk,purple_path) callcolor_replace_and(image_wrk,equals,equals,equals,65,65,65,255,255,255)callcolor_replace_and(image_wrk,equals,equals,equals,0,255,0,255,255,255)callcolor_replace_and(image_wrk,greater_than,equals,equals,150,0,255,0,255,0)callcolor_replace_and(image_wrk,equals,equals,equals,0,0,255,255,255,255)callcolor_replace_and(image_wrk,dont_care,less_than,less_than,0,255,255,255,255,255)callcolor_replace_and(image_wrk,dont_care,equals,dont_care,0,0,0,255,255,255)#if (show_EOP = 1) # call display_and_wait(image_wrk) #endif callpix_map = get_first_aoi(image_wrk,ALLCHAN,1,0) if (pix_map = 0)  jump@done_with_file endif call destroy_pixmap(AOI_wrk) call AOI_wrk =copy_pixmap callcolor_replace(image_tmp,greater_than,greater_than,greater_than,−1,−1,−1,255,255,255)aoinum = 1 @C4loop3  call show_AOI_bounding_box( ) # if (show_AOI =1)# call display_and_wait(AOI_wrk) # endif  call AOI_masked =get_pixmap_from_bbox(scan_org,0)  call image_tmp2 =composite_aoi(image_tmp,AOI_masked,255,255,255)  calldestroy_pixmap(image_tmp)  call image_tmp = copy_pixmap(image_tmp2) call destroy_pixmap(image_tmp2)  call destroy_pixmap(AOI_masked)  callpix_map = get_next_aoi( )  if (pix_map = 0)   call destroy_aoi_list( )  jump @C4Process3b  endif  call destroy_pixmap(AOI_wrk)  call AOI_wrk =copy_pixmap  aoinum = aoinum + 1  jump @C4loop3

A second pass is now made with all remaining objects in the image. Therules defined above can now eliminate objects identified in process 1. Asecond process that follows the logic rules will now create objects ofnew colors for the remaining objects of interest. The vectors of metricsof the transformed objects of interest are examined. Multiplequalitative approaches may be used in the evaluation of the objects,such as prototype performance and figure of merit. Metrics in thespatial domain, such as image amplitude (luminance, tristimulus value,spectral value) utilizing different degrees of freedom, the quantitativeshape descriptions of a first-order histogram, such as standarddeviation, mean, median, Skewness, Kurtosis, Energy and Entropy, % Colorfor red, green, and blue ratios between colors (total number of yellowpixels in the object/the total number of red pixels in the object),object symmetry, arithmetic encoder, wavelet transforms as well as otherhome made measurements are some, but not all, of the possiblemeasurements that can be used. Additional metrics can be created byapplying spectrally-based processes, such as Fourier, to the previouslymodified objects of interest or by analyzing eigenvalue produced from aPrincipal Components Analysis to reduce the dimension space of thevectors and remove outliers and non-representative data(metrics/images).

A color replacement technique is used to further emphasize tendencies ofcolor changes. For example, objects that contain a value on the redchannel >100, can be remapped to a level of 255 red so all bright redcolors are made pure red. This is used to help identify metal objectsthat have varying densities.

This can now help indicate the presence of a certain metal objectsregardless of its orientation in the image. It can also be correlated togeometric measurements using tools that determine boundaries and shapes.An example would be the correlation of the pixels with this red valuewith boundaries and centroid location. Other process may additionally beused as well.

The system and methods of the present invention are based on amethodology that is not restricted to a specific image type or imagingmodality. It is capable of identifying and distinguishing a broad rangeof object types across a broad range of imaging applications. It worksequally as well in applications such as CT scans, MRI, PET scans,mammography, cancer cell detection, geographic information systems, andremote sensing. It can identify and distinguish metal objects as well.

In medicine, the present invention is capable of, for example,distinguishing cancer cell growth in blood samples and is being testedwith both mammograms and x-rays of lungs. For example, FIG. 9 shows anoriginal input image with normal and cancerous cells. FIG. 10 shows theimage after the ITD process of the present invention has been applied,with only cancer cells showing up in green.

Another example of a medical application for the present invention isshown in FIGS. 11 and 12. FIG. 11 shows an original ophthalmology imageof the retina. FIG. 12 shows the image after the ITD process of thepresent invention have been applied, with the area of interest definedin red.

The analytical processing provided by the present invention can beextended to integrate data from a patient's familial history, bloodtests, x-rays, CT, PET (Positron Emission Tomography), and MRI scansinto a single integrated analysis for radiologists, oncologists and thepatient's personal physician. It can also assist drug companies inreducing costs by minimizing testing time for new drug certification.

B. Machine Learning Algorithms (MLA) Used for Image Classification

As discussed above, MLAs are responsible for generating the detectionsystem that determines if an object of interest is present. UsingMachine Learning Algorithms for image classification is herein referredto as “contextual imagery.” Contextual imagery not only focuses on thesegmented imaged, but on the entire image as well. Context often carriesrelevant and discriminative information that could determine if anobject of interest is present or not in the scene.

MLAs analyze the vectors of metrics taken from the images. The choice ofmetrics is important. Therefore, the feature extraction processpreferably includes “data conditioning” to statistically improve thedataset analyzed by the MLA.

Image conditioning is preferably carried out as part of the dataconditioning. Image conditioning is one of the first steps performed bythe image processing function. It initially consists of the removal ofobvious or almost obvious objects that are not one of the objects ofinterest from the image. By applying image processing functions to theimage, some important observations can also be made. For example, someunobvious portions of the object of interest may be distinguished fromother elements that are not part of the object of interest upon theapplication of certain types of image processing. These aspects of imageconditioning leverage the MLA's detection capability

Image normalization is preferably the first process applied to theimage. This consists of the removal of certain image characteristics,such as the artificial image enhancement (artifacts) that is sometimesapplied the system that created the image. Image normalization couldalso include removing image distortions created by the acquisitionsystem, as well as removal of intentional and unintentional artifactscreated by the software that constructed the image.

There are thousands of Machine Learning Algorithms including, but notlimited to, Kernel Systems such as the Support Vector Machines (SVMs)that are preferably used as one of the classification instruments. TheSVM approach exhibits the following advantages:

1. It can be used with data that has a complicated structure for which asimple separating hyperplane is not sufficient for classificationpurposes. A nonlinear separating surface between the classes can bedrawn with the SVM technique.

2. The separating surface is drawn by the SVM technique in an optimalway, maximizing the margin between the classes. In general, thisprovides a high probability that, with proper implementation, no otherseparating surface will provide better generalization performance withinthis framework.

3. Even when the amount of available data is small, the generalizationperformance is impressive.

4. The SVM technique is robust to small perturbations and noise in data.

5. A positive synergetic effect is often possible. This means thatadding image data collected from new objects of interest (e.g., newtypes of explosives) frequently results in a more efficient recognitionof images of objects of interest already included in the model.

In the case of a data set in which different classes are not linearlyseparated in the feature space, it is necessary to design a nonlinearseparating rule between them. However, this rule can be developed in aninfinite number of ways. For example, using a method of potentialfunctions, it is possible to reach 100% of the class separation for thetraining data set. At the same time, the respective model wouldtypically have a very poor generalization performance on the unseendata. This effect is commonly called ‘overfitting’. Thus, the goal is toavoid over-fitting while using the nonlinear approach.

To address this issue, the SVM technique relies on the following stages:

(1) mapping the initial feature vectors to a new feature space using anonlinear transformation; and

(2) applying a linear separating rule (a hyperplane) to vectors in thenew feature space.

The use of these two stages allows one to draw the nonlinear separatingsurface in the original feature space. The linear character of theseparating rule means, in general, better robustness and the possibilityof maximizing the margin between the classes explicitly.

An improved immunity to both noise and presence of possible outliers isprovided by introducing a “soft” margin. When a soft margin is used, apredetermined portion of training vectors are allowed to bemisclassified. Negative consequences of the over-fitting effect can besignificantly diminished or even completely averted by sacrificing thissmall portion of typically non-representative vectors. As a result, amuch better overall generalizing performance and robustness can beachieved in practical applications.

FIG. 13 is a flowchart of a method of creating an SVM model, inaccordance with one embodiment of the present invention. The methodstarts at step 600, where a nonlinear transformation type and itsparameters are chosen. The transformation is performed by the use ofspecific “kernels”, which are mathematical functions. Sigmoid, Gaussianor Polynomial kernels are preferably used.

Then, at step 610, a quadratic programming optimization problem for thesoft margin is solved efficiently. This requires a proper choice of theoptimization procedure parameters as well.

During the quadratic programming optimization procedure, some of themost representative vectors are selected from the pool of all vectorsavailable for training. These vectors are herein referred to as “SupportVectors.” The respective weights of the Support Vectors and a free term(a constant) are also calculated. This completes the SVM model.

FIG. 14 is a flowchart of a method of performing an SVM operation, inaccordance with one embodiment of the present invention. When apreviously unseen image is classified (any sub-image can also be usedinstead of the image), a feature generation technique is applied at step700 to yield a vector of the generated features that is used for theanalysis.

At step 710, a specified kernel transformation is applied to each of allpossible couples of the analyzed vector and a Support Vector. Thereceived values are weighted according to the respective weightcoefficients and added all together with the free term.

At step 720, the result of the kernel transformation is used to classifythe image. In a preferred embodiment, the image is classified as fallingin a first class (e.g., a threat) if the final result is larger than orequal to zero, and is otherwise classified as belonging to a secondclass (e.g., non-threat).

Although this framework was described in connection with two possibleclasses, it can be applied to multi-class classification problems withappropriate modification of the framework.

C. RGB-DNA Image Analysis

As discussed above, RGB-DNA is one of the image processing techniquesthat can be used in normalization step 400 and the image processing step410 (FIG. 7). The phrase “RGB-DNA”, as used herein, refers to arepresentation, in a predetermined color space, of most or all possiblevalues of colors which can be produced from a given image source. Thephrase “values of colors” is not limited to visual colors, but refers torepresentations of values, energies, etc. that can be produced by theimaging system. The use of RGB DNA for image analysis will be describedin detail in this section.

Physics of X-Ray Scanners and Color Images

Since the discovery of x-ray radiation in 1895 by W. C. Röentgen, theoutput of x-ray diagnostics equipment has been associated withgray-scaled images. Initially the photographic films were used tovisualize x-ray attenuation as a negative image. This technique is stillused today.

Later, fluorescent screens were employed to visualize the positiveimage. The digital imaging of detector-to-pixel design brought thepossibility of color highlighting based on one-to-one mapping of apredefined color palette into an original grayscale. In this case, thecolor image reflected x-ray attenuation in a more vivid way, as thegrayscale image did.

The invention of energy-selective or dual energy reconstruction,initially in medical x-ray diagnostics, made distinguishing Compton andphotoelectric fractions of attenuation with acceptable accuracypossible. As a result, the effective atomic number of materials Z_(eff)could be computationally reconstructed, in addition to the directmeasurement of attenuation alone, giving a clue about the chemicalstructure of the samples.

As shown in FIGS. 15A-15C, the images in medical diagnostics are usuallyvisualized on gray-scaled screens, as images of a doctor'schoice—conventional/standard (FIG. 15C), soft issues only (FIG. 15A), orbones only (FIG. 15B).

When vendors of baggage x-ray scanners adopted the dual energytechnique, they replaced the black and white monitors by the color ones.It was done to simplify the work of the screeners. Instead of analyzinga sequence of gray scaled images switching from conventional to lowenergy, high energy, Compton fraction, photoelectric fraction and back,a single color image was delivered. The colors of the image wereassigned to differentiate the chemical structure of materials accordingto their effective atomic numbers Z_(eff) and integral density d alongthe x-ray beam.

According to the recommendations of the United States TransportationSecurity Administration (TSA), shades of blue represent metal materials,shades of orange are assigned to organic compounds, and green lookingcolors are responsible for so called mixed or inorganic materials. FIGS.16A and 16B are x-ray images from a Smith Detection (Smith) x-rayscanner and a Rapiscan x-ray scanner, respectively. These are the twomost commonly used baggage x-ray scanners. The principal components ofany x-ray scanner are:

x-ray source with collimator;

array of detectors;

moving belt;

digital image formation and processing software; and

computing and visualization hardware.

FIG. 17 is a schematic diagram of a typical x-ray scanner. The scannerincludes an L-shaped detector array 810, a moving belt 820 for movingthe item being scanned 830 through the scanner 800, an X-ray source 840,a collimator 850 for collimating an X-ray beam 860 from the X-ray source840, and a photodiode assembly 865.

As shown in FIG. 18, the X-ray source 840 is typically implemented withan X-ray tubes that has a rotating anode 900, which is used forgenerating an uninterrupted flow of X-ray photons 910. The spectrum 920of the x-ray radiation is polychromatic, with a couple of peaks ofcharacteristic lines. For the baggage scanners of interest, the spectrumcovers a range from approximately 160 KeV to approximately 25 KeV.

The X-ray photons 910 of the beam 860 penetrate the materials in theitem being scanned 830, thereby experiencing attenuation of differentnatures (scattering, absorption etc.). Then, the x-ray beam 860 goesinto the L-shaped detector array 810 to be measured. The array 810 istypically a set of pre-assembled groups of detectors (16, 32 or 64detectors) positioned perpendicular to the x-ray beams 860.

Each individual detector is responsible for one row of pixels on thex-ray image. For energy-selective reconstruction, two detectors perpixel row are used, i.e., the high-energy detector is placed on the topof the low energy one. They are typically separated by a copper filter(typically <0.5 mm thick) installed for energy discrimination. Thisfilter is a crucial element of this technique. This paves a path forcalculating the Z_(eff) (effective atomic number) and d (integraldensity of the material) of the scanned object 830.

The moving belt 820 in the scanner 800 works as a slicing mechanism. Oneslice is one column of pixels. The speed of the belt should besynchronized with timing of the system to avoid distortion in lengthwisedimensions of the images.

An L-shaped detector array 810 causes clearly visible geometricdistortions in shapes. These distortions are the results of theprojection-detection scheme of a particular scanner design, which can beunderstood by simple geometrical constructions. FIGS. 19A and 19B areX-ray images from a Smith scanner and a Rapiscan scanner, respectively,which illustrate geometric distortions with colors. The distortions areparticularly apparent in the shapes of the frames 1000 and wheels 1010.

Another concern is the color representation of the dual energy imageitself. X-ray scanners of different vendors, with identical dimensionsand components, can deliver identical geometric appearance of shapes,but quite different colors for chemically identical scanned objects.These colors depend on the vendor's proprietary color scheme.

Nevertheless, as it will be described in more detail below, the RGB 3Dcolor schemes of different vendors can be mapped into a single universal2D (Z_(eff), d) space of physical parameters of Z_(eff) and d. Thepossibility of such mapping can be shown by looking at a mathematicaldescription of the dual energy technique, and by looking at the depth ofproprietary color schemes of two well known scanner vendors—SmithDetection and Rapiscan.

Mathematics of Dual Energy Technique without Colors

The two integral equations (1) and (2) below describe the flux of X-rayphotons F_(L)(θ) and F_(H)(θ) measured by low energy and high energydetectors, respectively, for the geometry shown in FIG. 20.

$\begin{matrix}{\mspace{79mu}{{\int_{E_{m\; i\; n}}^{E_{{ma}\; x}}{{\frac{r_{0}^{2}}{r_{L}^{2}(\theta)} \cdot {S\left( {\theta,r_{0},E} \right)} \cdot {\exp\left\lbrack {{- \frac{P}{E^{3}}} - {{f_{KN}(E)} \cdot C}} \right\rbrack}}\ {\mathbb{d}E}}} = {F_{L}(\theta)}}} & (1) \\{{\int_{E_{m\; i\; n}}^{E_{m\;{ax}}}{\frac{r_{0}^{2}}{r_{H}^{2}(\theta)} \cdot {S\left( {\theta,r_{0},E} \right)} \cdot {\exp\left\lbrack {{- \frac{P}{E^{3}}} - {{f_{KN}(E)} \cdot C}} \right\rbrack}\  \cdot {Q\left( {\theta,E} \right)} \cdot {\mathbb{d}E}}} = {F_{H}(\theta)}} & (2)\end{matrix}$where function

$\begin{matrix}{{P(\theta)} = {\int_{r_{0}}^{r_{L}{(\theta)}}{k_{p}\frac{\rho\left( {r,\theta} \right)}{A\left( {r,\theta} \right)}{{Z^{n}\left( {r,\theta} \right)} \cdot \ {\mathbb{d}r}}}}} & (3)\end{matrix}$is a photoelectric term or fraction of attenuation, and function

$\begin{matrix}{{C(\theta)} = {\int_{r_{0}}^{r_{L}{(\theta)}}{k_{c}\ \frac{\rho\left( {r,\theta} \right)}{A\left( {r,\theta} \right)}{{Z\left( {r,\theta} \right)} \cdot {\mathbb{d}r}}}}} & (4)\end{matrix}$is the Compton term of attenuation considered for every fixed value ofpolar angle θ. P(θ) and C(θ) are the desired solution we are lookingfor. The function of the energy selective (copper) filter is defined as

$\begin{matrix}{{Q\left( {\theta,E} \right)} = {\exp\left\lbrack {- {\int_{r_{L}{(\theta)}}^{r_{H}{(\theta)}}{{\mu_{f}\left( {\theta,r,E} \right)} \cdot \ {\mathbb{d}r}}}} \right\rbrack}} & (5)\end{matrix}$

The other symbols and definitions used in Equations (1) and (2) are asfollows:

-   -   S(θ,r₀,E)—the input flux of x-ray photons of energy E at the        surface with radius r₀;    -   r₀—the distance from the x-ray generator spot to the surface        where S is known;    -   r_(L)—the distance to the low energy detector;    -   r_(H)—the distance to the high energy detectors (r_(H)−r_(L) is        the thickness of the filter);    -   θ—polar angle    -   Z=Z_(eff)—the effective atomic number    -   ƒ_(KN)(E)—Kein-Nishina function of Compton attenuation energy        dependence;    -   ρ—physical mass density;    -   A—atomic weight;    -   ρ/A—density of atoms;    -   k_(p) and k_(c) are the constants dependent on the system of        units of measurements; and    -   n—empiric parameter (n=4 for our case).

For any given angle θ, the unknown variables are P, which is responsiblefor photoelectric, and C, which stands for Compton attenuation. Thisnonlinear system can be solved when Jacobian

$\begin{matrix}{J = {{\det\begin{pmatrix}\frac{\partial F_{L}}{\partial P} & \frac{\partial F_{L}}{\partial C} \\\frac{\partial F_{H}}{\partial P} & \frac{\partial F_{H}}{\partial C}\end{pmatrix}} \neq 0}} & (6)\end{matrix}$If P and C are found for a particular case of a uniform layer ofthickness L with ρ=const, Z=const, A=const, it means that:

$\begin{matrix}{{P\left( {x,y} \right)} = {{k_{p}\frac{\rho}{A}{Z^{n} \cdot L}} = {k_{p}{d \cdot Z^{n}}}}} & (7) \\{{{C\left( {x,y} \right)} = {{k_{c}\frac{\rho}{A}{Z \cdot L}} = {k_{c}{d \cdot Z}}}}{where}} & (8) \\{d = {\frac{\rho}{A} \cdot L}} & (9)\end{matrix}$is the integral density, and ratio

$\begin{matrix}{\frac{P}{C} = {\frac{k_{p}}{k_{c}}Z^{n - 1}}} & (10)\end{matrix}$does not depend on d. Therefore,

$\begin{matrix}{Z = \left( {\frac{P}{C}\frac{k_{c}}{k_{p}}} \right)^{1/{({n - 1})}}} & (11) \\{d = {{P/\left( {k_{p} \cdot Z^{n}} \right)} = {{C/\left( {k_{c} \cdot Z} \right)} = {C/\left\lbrack {k_{c} \cdot \left( {\frac{P}{C}\frac{k_{c}}{k_{p}}} \right)^{1/{({n - 1})}}} \right\rbrack}}}} & (12)\end{matrix}$

It can be seen that Z=const if the ratio P/C=const. In the (P,C) space,Z=const forms a straight line which goes from the point of origin, andthe tangent of the angle between the line and P axes is equals to C/P.The plot shown in FIG. 21 shows the lines in conditional units.

The surface Z=Z(P,C) is two-dimensional manifold in three-dimensional(P,C,Z) space, as shown in the plot of FIG. 22. The surface d=d(P,C) isa two-dimensional manifold in (P,C,d) as well, a shown in the plots ofFIGS. 23A and 23B, which are plots of 2D and 3D views, respectively, of(P,C) space with Zeff (P,C)=const.

The result derived above shows the straight and simple interpretation ofthe lines and points in the (P,C) space. Each point with coordinates Pand C in the space can be computed from the equations (1) and (2) if theright parts are measured correctly and Jacobian is nonzero. Each of thepoints reflects the effective atomic number Z and integral density d ofan object responsible for the measured right parts of the system.

Colors in Dual Energy Scanners without Mathematics

Any color image we see on the computer screen of a dual energy scanneris a 2D array of pixels with colors represented by (R,G,B) triplets.Each of these three values (R,G,B) belongs to the interval [0,255], andthe (R,G,B) set of all possible colors composes the 3D RGB space or cubeof 256³=16777216 discrete points. One can thus assume that the number ofunique colors needed to maintain an acceptable visual quality of a dualenergy color image can be quite large and approaches at least the numberof colors of a medium class digital camera ˜1500000. Nevertheless, itwas discovered that the number of unique colors in an average baggagecolor image is approximately 7,000 colors for a Smith HiScan 6040iscanner and less than 100,000 for a Rapiscan 515 scanner.

An aspect of the present invention is the development of tools tovisualize the set of unique colors, both as 3×2D projections to RG, GBand BR planes of the RGB cube, as shown in FIGS. 24A and 24B, and alsoas a 3D rotating view based on an OpenGL open source prototype, as shownin FIGS. 25A and 25B. FIGS. 24A and 24B are RGB_DNA 3×2D views for aSmith HiScan 6040i scanner and a Rapiscan 515 scanner, respectively.FIGS. 25A and 25B are 3D rotating views for a Smith HiScan 6040i scannerand a Rapiscan 515 scanner, respectively. The phrase “RGB_DN wasassigned to the discovered color schemes, where term “DNA” was usedbecause of the fact that all images, at least from the scanners of aparticular model, will inherit this unique set of RGB colors.

As discussed above, it is possible to map RGB_DNA to (P,C) and as suchbuild a bridge between (Z_(eff), d) and RGB_DNA. This provides a uniformway to work with images of different vendors regardless of their colorschemes.

FIG. 26 include plots of 2D (P,C) space (left plot) and 3D RGB_DNA(right plot) for a Smith scanner. It is clear that the point of origin(0,0) of (P,C) reflects the RGB point of (255,255,255) on a 3D view ofRGB_DNA. These points are responsible for the case of zero attenuation.

The next logical step consists of finding the relations between BlackPole (0,0,0) of the RGB_DNA and the Black Zone boundary of the (P,C)space. This point and the boundary are responsible for the scenario ofthe maximum possible measured attenuation. Beyond this point, thepenetration is so weak that detectors “can not see it at all”. In 3DRGB_DNA we have a single point-wise Black Pole, and in 2D (P,C) we havea stretched boundary. As shown in FIG. 27, the Black Zone boundary in(P,C) can be compressed/tightened to a single Black Pole or, what ismore practical and convenient, the Black Pole of 3D RGB_DNA can beexpanded and transformed to the curve, and together with unbent(piecewise-linear in our case) color curves of RGB_DNA, this 3D surfacecan be transformed to the 2D area similar to the 2D (P,C) space.

The next step that needs to be performed, is noting that the colorcurves on the Smiths 3D RGB_DNA surface and the straight lines of theZ_(eff)=const on (P,C) plane are actually the same entities. They arethe two-dimensional manifolds which are topologically equivalent, andcan be mutually mapped by a one-to-one relationship. This mapping forSmiths scanner is shown in FIG. 28. The Rapiscan scanner color schemecan be mapped to the (P,C) space in the same manner as continuouselastic deformation.

The simplest way to confirm that this hypothesis is correct, is tomeasure the colors resulting from scanning of the same material ofdifferent thickness, e.g., a wedge. If the hypothesis is correct, oneshould see the colors forming one color curve on the Smith RGB_DNA. FIG.29 shows a plot of the colors resulting from the scanning of a wedge ona Smith scanner, and verifies that the colors form one color curve onthe Smith RGB_DNA.

Overlapping and Color Algebra

The case discussed above was for a uniform of thickness L with ρ=const,Z=const, A=const. Increasing the thickness L results in increasing thevalues of P and C. The case of a non-uniform layer composed of two ormore uniform layers made of two or more different materials, as shown inFIG. 30, will now be addressed. In the case of two layers, thenon-uniform layer (L) can be expressed as L=L₁+L₂.

For fixed θ, we have

$\begin{matrix}{P = {{\int_{r_{0}}^{r_{L}{(\theta)}}{k_{p}\frac{\rho(r)}{A(r)}\ {{Z^{n}(r)} \cdot {\mathbb{d}r}}}} = {{\sum\limits_{k = 1}^{2}{\int_{L_{k}}{k_{p}\frac{\rho_{k}}{A_{k}}{Z_{k}^{n} \cdot \ {\mathbb{d}r}}}}} = {{\sum\limits_{k = 1}^{2}{k_{p}\frac{\rho_{k}}{A_{k}}Z_{k}^{n}L_{k}}} = {{\sum\limits_{k = 1}^{2}P_{k}} = {P_{1} + P_{2}}}}}}} & (13) \\{C = {{\int_{r_{0}}^{r_{L}{(\theta)}}{k_{c}\frac{\rho(r)}{A(r)}\ {{Z(r)} \cdot {\mathbb{d}r}}{\sum\limits_{k = 1}^{2}{\int_{L_{k}}{k_{p}\frac{\rho_{k}}{A_{k}}{Z_{k} \cdot \ {\mathbb{d}r}}}}}}} = {{\sum\limits_{k = 1}^{2}{k_{p}\frac{\rho_{k}}{A_{k}}Z_{k}L_{k}}} = {{\sum\limits_{k = 1}^{2}C_{k}} = {C_{1} + C_{2}}}}}} & (14)\end{matrix}$The fact that P=P₁+P₂ and C=C₁+C₂ can be interpreted as vector additionin (P,C) space, as shown in FIG. 31.

In the scenario in which a one-to-one mapping from (P,C) to RGB_DNA andback exists, and in which their colors are known, the RGB_DNA color ofthe overlapped materials can be calculated, as shown in FIG. 32.

Using vector subtraction, the color of one of the two overlappedmaterials can be found if the color of the second one and colorresulting from their overlapping is known. This technique of adding andsubtracting colors is referred to herein as “color algebra.” Coloralgebra is valid for any number K of overlapped layers:

$\begin{matrix}{P = {{\int_{r_{0}}^{r_{L}{(\theta)}}{k_{p}\frac{\rho(r)}{A(r)}\ {{Z^{n}(r)} \cdot {\mathbb{d}r}}}} = {{\sum\limits_{k = 1}^{K}{\int_{L_{k}}{k_{p}\frac{\rho_{k}}{A_{k}}{Z_{k}^{n} \cdot \ {\mathbb{d}r}}}}} = {{\sum\limits_{k = 1}^{K}{k_{p}\frac{\rho_{k}}{A_{k}}Z_{k}^{n}L_{k}}} = {\sum\limits_{k = 1}^{K}P_{k}}}}}} & (15) \\{C = {{\int_{r_{0}}^{r_{L}{(\theta)}}{k_{c}\frac{\rho(r)}{A(r)}\ {{Z(r)} \cdot {\mathbb{d}r}}}} = {{\sum\limits_{k = 1}^{K}{\int_{L_{k}}{k_{p}\frac{\rho_{k}}{A_{k}}{Z_{k} \cdot \ {\mathbb{d}r}}}}} = {{\sum\limits_{k = 1}^{K}{k_{p}\frac{\rho_{k}}{A_{k}}Z_{k}L_{k}}} = {\sum\limits_{k = 1}^{K}C_{k}}}}}} & (16)\end{matrix}$

Equations (11) and (12) above express the effective atomic number Z anddensity d as functions of P and C for a single uniform layer of amaterial. In the case of K layers of different materials with theeffective atomic numbers Z_(k) and densities d_(k) k=1, . . . , K, theformulas for Z and d can be derived from

$\begin{matrix}{P_{k} = {k_{p}\frac{\rho_{k}}{A_{k}}Z_{k}^{n}L_{k}}} & (17) \\{{C_{k} = {k_{p}\frac{\rho_{k}}{A_{k}}Z_{k}L_{k}}}{and}} & (18) \\{P = {\sum\limits_{k = 1}^{K}P_{k}}} & (19) \\{C = {\sum\limits_{k = 1}^{K}C_{k}}} & (20)\end{matrix}$using substitution

$d_{k} = {\frac{\rho_{k}}{A_{k}}L_{k}}$as a density for the layer k:

$\begin{matrix}{P = {{k_{p}{d \cdot Z^{n}}} = {\sum\limits_{k = 1}^{K}{k_{p}d_{k}Z_{k}^{n}}}}} & (21) \\{{C = {{k_{c}{d \cdot Z}} = {\sum\limits_{k = 1}^{K}{k_{p}d_{k}Z_{k}}}}},} & (22)\end{matrix}$the expression for the resulting Z and d can be found:

$\begin{matrix}{Z = \left( \frac{\sum\limits_{k = 1}^{K}{d_{k}Z_{k}^{n}}}{\sum\limits_{k = 1}^{K}{d_{k}Z_{k}}} \right)^{1/{({n - 1})}}} & (23) \\{d = \left\lbrack \frac{\left( {\sum\limits_{k = 1}^{K}{d_{k}Z_{k}}} \right)^{n}}{\sum\limits_{k = 1}^{K}{d_{k}Z_{k}^{n}}} \right\rbrack^{1/{({n - 1})}}} & (24)\end{matrix}$

Equations (23) and (24) are the mathematical expressions fordecomposition of the initial Z and d into several components withdifferent Z_(k) and d_(k), k=1, . . . , K. These formulas built thefoundation for the potential solution of the inverse problem ofmulti-layer material detection in x-ray scanning machines.

Limitation of Visual Perception of Digital Images

Explosive detection using the methodology described above has beentested on images stored in 24-bit bitmap (bmp) format. These images weresupposed to be exact copies from the computer screen of x-ray scanners.However, in several cases, the images were not what they were supposedto be despite the fact that the images passed visual inspection byhumans. Identical for human perception but different in their pixel'sRGB content, these images confused the system functionality and had notbeen caught until they were forced to go through RGB_DNA viewers.

FIG. 33 shows examples of images with their 3D RGB_DNA views. Only theimage on the far left is in correct original RGB_DNA colors. The othertwo images are visually undistinguished from first one. Nevertheless,they are in fact bmp images converted back from gif and jpeg conversionsof an original bmp image.

Another example, shown in FIG. 34, shows accidental conversion from24-bit bmp to 16-bit and back. FIGS. 34 and 32 can be compared to seethe difference between the incorrect RGB_DNA and the correct one.

The fact that number of RGB_DNA colors in color images of dual energyx-ray scanners is fixed for each model and are much less than 16,777,216RGB triplets in 24-bit bmp, it is possible to make automated inspectionof incoming images without the actual visual review of their RGB_DNA(3×2D or 3D). This process can detect the presence of images not createdwith that x-ray scanner or the scanner is out of calibration. Theexistence of RGB_DNA itself as a limited subset of the entire 24-bit RGBset makes it possible. The component designed and implemented for thispurpose performs a fast search through already collected RGB_DNA setsfor each pixel of an incoming image, and assures that the system willnot be confused.

The Colors of Z_(eff)=Const Z-Lines Extraction

The color scheme of the Smith scanner is comprised of 29 color curvesthat are stretched from white RGB pole (255,255,255) to black pole(0,0,0). There is one more line of gray colors used for edgeenhancement, but these colors do not represent any materials. Asdiscussed above, the color component can determine that the RGB color ofa pixel belongs to the RGB_DNA whole set of colors, but it can notdetermine which one of the 29 curves this color is a part.

As discussed above, each color curve represents the line in (P,C) spacewith Z_(eff)=const. They are referred to herein as “z-lines.” If thecolors of each line are known, it is possible to exploit this fact forat least two very useful applications. The first application is thephysics-based feature vectors computation in pattern classificationalgorithms, which will be discussed in more detail below.

The second application uses z-lines for removing or keeping selectedmaterials from an image. This is a much more flexible image filteringtool than so called “organic and metal stripping” provided by x-rayscanner manufacturers, as will be discussed in more detail below.

Z-lines are clearly visible on RGB_DNA 3D view (see FIGS. 25A and 26)and they can be extracted without any difficulties. Nevertheless, thereare several confusing facts. For example, in the areas close to polar(white and black) zones, the number of RGB_DNA colors can be less than29 (the actual number of lines). Another surprise is the fact thatz-lines themselves are actually not lines. They are integerapproximation of the ideal continuous 3D lines by the finite set ofpoints with integer three coordinates. Therefore, there are cases wherethree dimensional aliasing resembles 3D stares in RGB cube. In suchcases, the procedure of extracting RGB coordinates of points for z-linesis not straightforward. FIG. 35 shows the fine structure of z-lines ontheir way from the central region of the 3D RGB cube towards the blackpole with RGB=(0,0,0). As can be seen, the aliasing gets worse closer topoles. The picture appears so complicated it is difficult to determinewhether the 3D RGB cube is the native home for z-lines.

One can look at z-lines from another point. That is, from the point inRGB space lying on the prolongation of the major diagonal of RGB cube,as shown in FIG. 36. One can see that each z-line seems to be a planeline, and the plane goes through the major diagonal. In a cylindricalsystem of coordinates (z, r, θ) with z coincided with the majordiagonal, each z-line has its very narrow sector of the angularcoordinates θ for all its points. One can say with good accuracy thatthe z-line for a particular Z_(eff)=const contains the points withθ=const. Therefore, the cylindrical system of coordinates is morenatural or, at least, more convenient.

In this system, the angular coordinate θ is an invariant for all pointsof the same z-line. This means that HSI color space is more suitable, ormore natural, for z-lines than RGB, and extraction of z-line's colors isa straightforward operation universal, not only for the Smith colorscheme, but for the Rapiscan color scheme as well.

FIG. 37 shows z-line numbers 3 and 15 together with their respectivecolors. FIG. 38 shows a 3D view for extracted z-line numbers 1, 7 and 25with respective colors.

Having z-lines extracted and sorted by intensity value I of HSI, one isable to navigate in color RGB_DNA space like in (P,C) space. For any twocolors, one can say which one has a greater effective atomic numberZ_(eff) corresponding to their colors or, in case of the same Z_(eff),one can say which one is more dense. Moreover, one can extend themeaning of hue coordinate H of HSI to be the carrier of Z_(eff) andintensity I to be responsible for density of a material.

Saturation S is thus far unemployed. It can be an unemployed freeparameter (and is for Smith and Rapiscan scanners) responsible forcarrying the proprietary “look and feel” of the color scheme. Colors ofthe same objects can appear differently on Smith and Rapiscan scannershaving the same or close H and I, but different S.

Physics Based Feature Vectors Z-Metrics

Results of feature extraction for color images depends on the colors ofan image, the color scheme (RGB, HIS or other) and the algorithm of thefeatures computation itself. Mapping z-lines and their ordered colors to(P,C) space opens up an opportunity to exclude color from the featureextraction process. Instead of using three variables of a particularcolor space, such as R, G, and B in RGB, to feed the feature extractionalgorithm, two variables of (P,C) can be used.

Two dimensions reduce complexity. Unlike of points in color spaces, thepoints in (P,C) space have clear physical meaning. P stands forPhotoelectric fraction of attenuation and C stands for Comptonattenuation. To exploit these advantages, the methodology of z-metricsimplemented. Z-metrics is actually the set of 29 histograms, one pereach z-line. It can be computed with bins or without bins, weighed ornot. Experiments have shown that this metric alone is as effective as anassembly of several metrics based on traditional features of colorimages. FIG. 39 is a plot of fragment of typical 25 bin's z-metrics forthe first 9 z-lines.

Beyond Organic and Metal Stripping Z-Filters

Manufacturers of dual energy x-ray machines advertise the “materialstripping” feature of their scanners. FIG. 40 shows an example of thisfeature, together with 3D views of the respective RGB_DNA. It is obviousthat stripping is a result of simple color replacement of colors from“orange” or “blue” z-lines by gray colors, and it can be considered as amanufacturer's proof of the idea that z-lines are actually the lines ofZ_(eff)=const.

Organic or metal stripping, as is easy to see, are only very limitedsimple special cases from an unlimited number of other possibilities.The colors mapped to any region in (P,C) space can be replaced, i.e.,z-filtered. Alternatively, they can be processed in some other way. Thekey point is the mapping itself. If one has the mapping, one can applyz-filters of any kind, like those shown in FIGS. 41-45.

The image analysis system 130 can be implemented with a general purposecomputer. However, it can also be implemented with a special purposecomputer, programmed microprocessor or microcontroller and peripheralintegrated circuit elements, ASICs or other integrated circuits,hardwired electronic or logic circuits such as discrete elementcircuits, programmable logic devices such as FPGA, PLD, PLA or PAL orthe like. In general, any device on which a finite state machine capableof executing code for implementing the process steps of FIG. 7 can beused to implement the image analysis system 130.

Input channel 110 may be, include or interface to any one or more of,for instance, the Internet, an intranet, a PAN (Personal Area Network),a LAN (Local Area Network), a WAN (Wide Area Network) or a MAN(Metropolitan Area Network), a storage area network (SAN), a frame relayconnection, an Advanced Intelligent Network (AIN) connection, asynchronous optical network (SONET) connection, a digital T1, T3, E1 orE3 line, Digital Data Service (DDS) connection, DSL (Digital SubscriberLine) connection, an Ethernet connection, an ISDN (Integrated ServicesDigital Network) line, a dial-up port such as a V.90, V.34bis analogmodem connection, a cable modem, and ATM (Asynchronous Transfer Mode)connection, or an FDDI (Fiber Distributed Data Interface) or CDDI(Copper Distributed Data Interface) connection. Input channel 110 mayfurthermore be, include or interface to any one or more of a WAP(Wireless Application Protocol) link, a GPRS (General Packet RadioService) link, a GSM (Global System for Mobile Communication) link, CDMA(Code Division Multiple Access) or TDMA (Time Division Multiple Access)link such as a cellular phone channel, a GPS (Global Positioning System)link, CDPD (Cellular Digital Packet Data), a RIM (Research in Motion,Limited) duplex paging type device, a Bluetooth radio link, or an IEEE802.11-based radio frequency link. Input channel 110 may yet further be,include or interface to any one or more of an RS-232 serial connection,an IEEE-1394 (Firewire) connection, a Fiber Channel connection, an IrDA(infrared) port, a SCSI (Small Computer Systems Interface) connection, aUSB (Universal Serial Bus) connection or other wired or wireless,digital or analog interface or connection.

The foregoing embodiments and advantages are merely exemplary, and arenot to be construed as limiting the present invention. The presentteaching can be readily applied to other types of apparatuses. Thedescription of the present invention is intended to be illustrative, andnot to limit the scope of the claims. Many alternatives, modifications,and variations will be apparent to those skilled in the art. Variouschanges may be made without departing from the spirit and scope of thepresent invention, as defined in the following claims.

1. A method for determining whether there is an anomaly in data,comprising: performing one of applying a nonlinear divergence transformto the data, mapping the data to a predetermined color space using afirst nonlinear transformation and mapping the data to a feature spaceusing a second nonlinear transformation to yield altered data, whereinthe nonlinear divergence transform, first nonlinear transformation andsecond nonlinear transformation each comprises at least one pointoperation having at least one nodal point that is adjusted so as toeffect the divergence of a feature of interest from other features; andcomparing the altered data with a template of altered data created froma set of data not containing the anomaly to determine whether there is adifference between the altered data and the template, said differencecorresponding to said anomaly; wherein the template of altered data iscreated by applying one of the nonlinear divergence transform to the setof data, mapping the set of data to the predetermined color space usingthe first nonlinear transformation and mapping the set of data to thefeature space using the second nonlinear transformation.
 2. The methodof claim 1, further comprising repeating the performing and comparingsteps using a different one of the applying and mapping steps if thecomparing step does not produce a difference corresponding to theanomaly.
 3. The method of claim 1, wherein the data comprises x-raydata.
 4. The method of claim 1, wherein the data comprises hyperspectraldata.
 5. The method of claim 4, wherein the hyperspectral data comprisestwo-dimensional hyperspectral data.
 6. The method of claim 4, whereinthe hyperspectral data comprises three-dimensional hyperspectral data.7. The method of claim 4, wherein the hyperspectral data comprises x-rayhyperspectral data.
 8. The method of claim 1, wherein the data comprisesan image.
 9. The method of claim 8, wherein the image comprises an x-rayimage.
 10. The method of claim 8, wherein the image comprises aninfrared image.
 11. The method of claim 8, wherein the image comprises amagnetic resonance image.
 12. The method of claim 8, wherein the imagecomprises a positron emission tomography image.
 13. The method of claim8, wherein the image comprises a laser radar image image.
 14. The methodof claim 8, wherein the image comprises an ultrasound image.